Читать книгу Advanced Antenna Array Engineering for 6G and Beyond Wireless Communications - Richard W. Ziolkowski - Страница 23

A simple, yet powerful, analog method to create steerable and multiple beams is to employ a spherical Luneburg lens. A Luneburg lens in its simplest form consists of a radially inhomogeneous sphere with a well‐defined graded dielectric constant that varies from 2.0 at the center of the sphere to 1.0 at its outer surface. The gradation is given by the equation: , where ε_r is the relative dielectric constant at radius r and a is the outer radius of the sphere. The resulting structure serves to transform rays incident on one side to parallel rays on the opposite side. An antenna feed located on the surface of the lens produces a steered beam if the element moves around the surface as illustrated in Figure 1.8a. The low dielectric constant near the lens surface ensures that no energy is reflected back to the feed. In order to accommodate feeds whose phase centers cannot be placed at the surface of the Luneburg lens, such as a horn antenna, one can modify the distribution of the dielectric constant within the lens [15]. Figure 1.8b shows the corresponding cylindrical version, which is known as a cylindrical Luneburg lens.

Figure 1.8 Illustration of Luneburg lenses. (a) Spherical. (b) Cylindrical.

The beamwidth of a Luneburg lens is approximately the same as that of a linear array whose length equals the diameter of the lens. Nevertheless, the nulls are considerably deeper. If one places a number of feeds along the surface of a Luneburg lens, one can produce a multiple beam antenna, one beam per feed. These multi‐beam antennas can be employed for data distribution or broadcasting in 5G networks.

It is very difficult and very costly to produce an ideal Luneburg lens. As a practical alternative, one can employ several separate shells to replace the theoretical continuous gradation of the dielectric constant with a discrete approximation to it. Many such versions have been deployed in a variety of current systems.

The main advantages of Luneburg lenses over antenna arrays based on beamforming networks can be summarized as follows [14]:

 A great simplification in component count and inherent low passive intermodulation (PIM).

 Reduction of network losses.

 Beam crossover levels can be selected arbitrarily by choosing the spacing of the source elements.

 Isolation between elements is generally superior to that obtained with beamforming networks.

The relative disadvantage of a Luneburg lens antenna is its three‐dimensional bulk compared with planar forms of the array antennas. Nevertheless, some mobile operators are currently showing strong interest in Luneburg lenses due to their low cost in hardware and low energy consumption.